Finite Group Databasebeta

← #10576721

Subgroups — #10576721

Order 512.

6793 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62815C212yesmaximal, complemented
2#61424C218yesmaximal, complemented
3#61423C218yesmaximal, complemented
4#61422C214yesmaximal, complemented
5#61421C214yesmaximal, complemented
6#61420C214yesmaximal, complemented
7#61419C214yesmaximal, complemented
8#61401C214yesmaximal, complemented
9#61401C218yesmaximal, complemented
10#61393C214yesmaximal, complemented
11#60643C212yesmaximal, complemented
12#60639C211yesmaximal, characteristic, complemented
13#60422C214yesmaximal, complemented
14C2×#3035C212yesmaximal, complemented
15C2×#2962C211yesmaximal, characteristic, complemented
16#60161C212yesmaximal, complemented
17C4×#575C211yesmaximal, characteristic, complemented
18C2×#575C2212yes—
19C2×#575C2211yescharacteristic
20C2×#575C2212yes—
21C22×#135C2214yes—
22#3512—24no—
23#3511—22no—
24#3511—22no—
25#3510C2218yescomplemented
26#3509C2214yescomplemented
27#3508C2214yescomplemented
28#3507C2214yescomplemented
29#3507C2214yescomplemented
30#3506C2214yescomplemented
31#3506C2214yescomplemented
32#3505—24no—
33#3505—24no—
34#3480C2218yescomplemented
35#3480C2218yescomplemented
36#3475—24no—
37#3475—24no—
38#3455—24no—
39#3449C2214yes—
40#3444—24no—
41C2×#533C2211yescharacteristic
42C2×#532C2212yes—
43#3428C2214yes—
44C2×C4×#41C2212yes—
45#3403C22116yescomplemented
46#3403C2218yescomplemented
47#3402C22116yescomplemented
48#3402C2218yescomplemented
49#3401C22116yescomplemented
50#3401C22116yescomplemented
51#3401C22116yescomplemented
52#3400C22116yescomplemented
53#3400C2218yescomplemented
54#3399C2218yescomplemented
55#3399C22116yescomplemented
56#3398C2218yescomplemented
57#3398C22116yescomplemented
58#3397C2218yescomplemented
59#3397C22116yescomplemented
60#3396C2214yescomplemented
61#3396C2218yescomplemented
62#3395C2214yescomplemented
63#3394C2218yescomplemented
64#3394C22116yescomplemented
65#3393C2214yescomplemented
66#3393C2218yescomplemented
67#3392C2218yescomplemented
68#3391C2214yescomplemented
69#3156C2218yescomplemented
70#3155C2218yescomplemented
71#3154C2218yescomplemented
72#3154C2218yescomplemented
73#3153C2218yescomplemented
74#3152C2214yescomplemented
75#3151C2214yescomplemented
76#3150C2214yescomplemented
77#3150C2218yescomplemented
78#3147C2214yescomplemented
79#3147C2218yescomplemented
80#3046C2218yescomplemented
81#3046C2218yescomplemented
82#3045C2218yescomplemented
83#3045C2218yescomplemented
84#3044C2218yescomplemented
85#3043C2218yescomplemented
86#3042C2218yescomplemented
87#3041C2218yescomplemented
88#3035C2214yes—
89#3035C2214yes—
90#3035C2218yes—
91#3035C22116yescomplemented
92#3035C22116yescomplemented
93#3035C2214yescomplemented
94#3035C2214yescomplemented
95#3035C2218yescomplemented
96C2×#464C2214yescomplemented
97C2×#462C2212yescomplemented
98C2×#460C2212yescomplemented
99C2×#463C2214yescomplemented
100C2×#461C2212yescomplemented
101C2×#459C2212yescomplemented
102#2962C2214yescomplemented
103#2962C2214yescomplemented
104#2962C2218yescomplemented
105C2×#446C2212yescomplemented
106C2×#446C2214yescomplemented
107C2×C8×Q8C2212yescomplemented
108#2947C2218yescomplemented
109#2947C2218yescomplemented
110#2946C2218yescomplemented
111#2946C2218yescomplemented
112C4×#137C2214yescomplemented
113C4×#137C2214yescomplemented
114C4×AGL(1,ℤ/8)C2214yescomplemented
115C4×AGL(1,ℤ/8)C2214yescomplemented
116#2943C2218yescomplemented
117#2943C2214yescomplemented
118C4×#135C2218yescomplemented
119C4×#135C2214yescomplemented
120#2911C2211yescharacteristic
121C2×#424C2212yes—
122C22×C4⋊C8C2211yescharacteristic
123#2896C2212yes—
124C2×#416C2214yes—
125C2×#405C2212yes—
126C2×C4×M16C2211yescharacteristic
127C22×#41C2314yes—
128C22×#41C2312yes—
129#575—216no—
130#575—28no—
131#575—48no—
132C2×#137C2318yes—
133C2×#137C2314yes—
134C2×#137C2318yes—
135C2×AGL(1,ℤ/8)C2318yes—
136C2×AGL(1,ℤ/8)C2314yes—
137C2×AGL(1,ℤ/8)C2318yes—
138C2×#135—416no—
139C2×#135C2318yes—
140C2×#135C2314yes—
141C2×#135C2318yes—
142C2×#135C2318yes—
143C2×#135C2318yes—
144C2×#135C2318yes—
145C2×#135C2318yes—
146C22×Q16C2314yes—
147C22×SD16C2314yes—
148C22×SD16C2314yes—
149C22×D8C2314yes—
150C22×M16C2311yescharacteristic
151C22×M16C2311yescharacteristic
152C23×C8C2312yes—
153#559C2318yes—
154#559C23116yes—
155#559C23116yes—
156#559C2318yes—
157#557C2318yes—
158#557C2318yes—
159#556—24no—
160#556—24no—
161#556C2318yes—
162#556C23116yes—
163#556C23116yes—
164#556C2318yes—
165#555—24no—
166#555—24no—
167#554—24no—
168#554—24no—
169#553—28no—
170#553—28no—
171#553—28no—
172#553—28no—
173#553—216no—
174#553—216no—
175#552—28no—
176#552—28no—
177#552—28no—
178#552—28no—
179#551—216no—
180#551—216no—
181#550C2318yes—
182#550C2318yes—
183#548—28no—
184#548—28no—
185#547—24no—
186#547—24no—
187#546—28no—
188#546—28no—
189#542—28no—
190#542—28no—
191#541—28no—
192#540—28no—
193#539—28no—
194#539—28no—
195#538—28no—
196#538—28no—
197#537—24no—
198#537—24no—
199#536C2318yes—
200#536C2318yes—
201#535C2318yes—
202#535C2318yes—
203#534—28no—
204#533—24no—
205#533—24no—
206#533D414yes—
207#533D414yes—
208#533C2314yes—
209#533C2314yes—
210#532—24no—
211#532—24no—
212#532—22no—
213#532—22no—
214#532—22no—
215#532—22no—
216#532C2314yes—
217#532C23116yes—
218#532C2314yes—
219#532C2314yes—
220#532C2314yes—
221C2×C4⋊Q8D411yescharacteristic
222C2×C4⋊Q8D411yescharacteristic
223C2×C4⋊Q8C2312yes—
224C2×#127C2312yes—
225#529—28no—
226#529—28no—
227#529—28no—
228#529—28no—
229#529—28no—
230#529—28no—
231#529—216no—
232#529—216no—
233C2×#125D412yes—
234C2×#124C2314yes—
235#525—28no—
236#525—28no—
237#525—28no—
238#525—28no—
239C2×C22⋊Q8D412yes—
240C2×C22⋊Q8D412yes—
241C2×#121—22no—
242C2×#121—22no—
243#520—24no—
244#520—24no—
245#520C2318yes—
246#520C2318yes—
247#519C2318yes—
248#518—28no—
249#518C2318yes—
250C4×#41—28no—
251C4×#41—28no—
252C4×#41—28no—
253C4×#41—22no—
254C4×#41—22no—
255C4×#41—22no—
256C4×#41—22no—
257C4×#41C2314yes—
258C4×#41C2314yes—
259C4×#41C2314yes—
260C4×#41C2314yes—
261C4×#41C23116yes—
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2312yes—
264C2×C4×Q8C2312yes—
265C2×C4×Q8C2312yes—
266C2×C4×D4—22no—
267C2×C4×D4—22no—
268C2×C4×D4—22no—
269C2×C4×D4—22no—
270C2×C4×D4C2312yes—
271C2×C4×D4C2312yes—
272C2×#117—28no—
273C2×#117—22no—
274C2×#117C2312yes—
275C2×#117C2312yes—
276C22×C42—22no—
277C22×C42C2311yescharacteristic
278#497C23116yes—
279#497C23116yes—
280#497C23116yes—
281#496C23116yes—
282#496C23116yes—
283#496C23116yes—
284#495C2318yes—
285#495C2318yes—
286#495C2318yes—
287#495C2318yes—
288#495C23116yes—
289#494C2314yes—
290#494C2318yes—
291#493C2314yes—
292#493C2318yes—
293#492C2318yes—
294#492C23116yes—
295#464C2318yes—
296#464C23116yes—
297#464C23116yes—
298#464C2318yes—
299#464C23116yes—
300#464C2318yes—
301#464C23116yes—
302#464C2318yes—
303#463C2318yes—
304#463C23116yes—
305#463C23116yes—
306#463C2318yes—
307#463C23116yes—
308#463C2318yes—
309#463C23116yes—
310#463C2318yes—
311#462C2314yes—
312#462C23116yes—
313#462C2314yes—
314#462C23116yes—
315#462C2318yes—
316#461C2314yes—
317#461C23116yes—
318#461C2314yes—
319#461C23116yes—
320#461C2318yes—
321#460C2314yes—
322#460C23116yes—
323#460C2318yes—
324#460C23116yes—
325#460C2314yes—
326#459C2314yes—
327#459C23116yes—
328#459C2314yes—
329#459C23116yes—
330#459C2318yes—
331#446C2318yes—
332#446C23116yes—
333#446C23116yes—
334#446C2318yes—
335C8×Q8C2314yes—
336C8×Q8C2314yes—
337C8×Q8C2318yes—
338#442C2318yes—
339#442C23116yes—
340#441C2318yes—
341#441C23116yes—
342#440C2318yes—
343#440C23116yes—
344#440C23116yes—
345#440C2318yes—
346C4×Q16C2318yes—
347C4×Q16C2314yes—
348C4×Q16C2314yes—
349C4×Q16C2318yes—
350C4×SD16C2318yes—
351C4×SD16C23116yes—
352C4×SD16C23116yes—
353C4×SD16C2318yes—
354C4×D8C2314yes—
355C4×D8C2318yes—
356C4×D8C2318yes—
357C4×D8C2314yes—
358#428C2314yes—
359#428C2314yes—
360#427C2314yes—
361#424C2318yes—
362#424C2318yes—
363C2×C4⋊C8C2311yescharacteristic
364C2×C4⋊C8C2311yescharacteristic
365C2×C4⋊C8C2312yes—
366C2×C4⋊C8C2312yes—
367C2×C4⋊C8C2312yes—
368C2×C4⋊C8C2314yes—
369C2×C4⋊C8C2314yes—
370C2×C4⋊C8C2314yes—
371#419C2314yes—
372#418C2314yes—
373#417C2314yes—
374#417C2314yes—
375#416C2318yes—
376#416C2318yes—
377#416C2318yes—
378#416C2318yes—
379#416C2318yes—
380C2×#103C2314yes—
381C2×#103C2314yes—
382C2×#102C2314yes—
383C2×#102C2314yes—
384#405C2318yes—
385#405C2318yes—
386C4×M16C2314yes—
387C4×M16C2314yes—
388C2×#97C2312yes—
389C2×#97C2314yes—
390C2×C4×C8C2312yes—
391C2×C4×C8C2314yes—
392C2×#41—28no—
393C2×#41—28no—
394C2×#41—22no—
395C2×#41—24no—
396C2×#41—22no—
397C2×#41—24no—
398C2×#41—216no—
399C2×#41—28no—
400C2×#41—28no—
401C2×#41—216no—
402C2×#41C2414yes—
403C2×#41C2418yes—
404C2×#41C2414yes—
405C2×#41C2418yes—
406C22×Q8C2×D412yes—
407C22×Q8C2×D412yes—
408C22×Q8C2412yes—
409C22×Q8C2414yes—
410C22×D4—22no—
411C22×D4—24no—
412C22×D4—22no—
413C22×D4—22no—
414C22×D4C2412yes—
415C22×D4C2414yes—
416C23×C4—24no—
417C23×C4—22no—
418C23×C4—22no—
419C23×C4—22no—
420C23×C4C2×D411yescharacteristic
421C23×C4C2×D411yescharacteristic
422C23×C4C2411yescharacteristic
423#137—232no—
424#137—216no—
425#137—416no—
426AGL(1,ℤ/8)—232no—
427AGL(1,ℤ/8)—216no—
428AGL(1,ℤ/8)—416no—
429#135—232no—
430#135—216no—
431#135—416no—
432#135—416no—
433#135—416no—
434#135—416no—
435#135—416no—
436C2×Q16—48no—
437C2×Q16C2418yes—
438C2×Q16C2414yes—
439C2×Q16C2418yes—
440C2×Q16C2418yes—
441C2×Q16C2418yes—
442C2×SD16—48no—
443C2×SD16—48no—
444C2×SD16C24116yes—
445C2×SD16C2418yes—
446C2×SD16C2418yes—
447C2×SD16C2418yes—
448C2×SD16C2418yes—
449C2×SD16C2418yes—
450C2×SD16C24116yes—
451C2×D8—48no—
452C2×D8C2418yes—
453C2×D8C2414yes—
454C2×D8C2418yes—
455C2×D8C2418yes—
456C2×D8C2418yes—
457C2×M16—24no—
458C2×M16#4118yescomplemented
459C2×M16C2414yes—
460C2×M16C2414yes—
461C22×C8—28no—
462C22×C8C2414yes—
463C22×C8C2414yes—
464C22×C8C2412yes—
465C22×C8C2412yes—
466C22×C8C2412yes—
467C22×C8C2412yes—
468C4⋊Q8—22no—
469C4⋊Q8—22no—
470C4⋊Q8C2×D414yes—
471C4⋊Q8C2×D414yes—
472C4⋊Q8C2×D414yes—
473C4⋊Q8C2×D414yes—
474C4⋊Q8C2414yes—
475C4⋊Q8C2414yes—
476C4⋊Q8C24116yes—
477#127—22no—
478#127—22no—
479#127C2414yes—
480#127C2414yes—
481#127C24116yes—
482#126—216no—
483#126—216no—
484#126—216no—
485#126—216no—
486#126—216no—
487#126—216no—
488#125—28no—
489#125—28no—
490#125—216no—
491#125—216no—
492#125C2×D418yes—
493#125C2×D418yes—
494#124—28no—
495#124—28no—
496#124—216no—
497#124—216no—
498#124—24no—
499#124—24no—
500#124C2418yes—
501#124C2418yes—
502#124C24116yes—
503#124C24116yes—
504#123—216no—
505#123—216no—
506#123—216no—
507#123—216no—
508#123—216no—
509#123—216no—
510#123—216no—
511#123—216no—
512C22⋊Q8—28no—
513C22⋊Q8—28no—
514C22⋊Q8—216no—
515C22⋊Q8—216no—
516C22⋊Q8—28no—
517C22⋊Q8—28no—
518C22⋊Q8—28no—
519C22⋊Q8—28no—
520C22⋊Q8C2×D418yes—
521C22⋊Q8C2×D418yes—
522C22⋊Q8C2×D418yes—
523C22⋊Q8C2×D418yes—
524#121—24no—
525#121—24no—
526#121—24no—
527#121—24no—
528#121—24no—
529#121—24no—
530#121—24no—
531#121—24no—
532#121—216no—
533#121—216no—
534#121—28no—
535#121—28no—
536#121—28no—
537#121—28no—
538#121—28no—
539#121—28no—
540#121—216no—
541#121—216no—
542#120—216no—
543#120—216no—
544C4×Q8—28no—
545C4×Q8—28no—
546C4×Q8—28no—
547C4×Q8—28no—
548C4×Q8—22no—
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—22no—
552C4×Q8C2×D414yes—
553C4×Q8C2×D418yes—
554C4×Q8C2×D414yes—
555C4×Q8C2414yes—
556C4×Q8C2414yes—
557C4×Q8C2414yes—
558C4×Q8C2414yes—
559C4×Q8C24116yes—
560C4×Q8C24116yes—
561C4×Q8C2414yes—
562C4×Q8C2418yes—
563C4×Q8C2414yes—
564C4×D4—24no—
565C4×D4—24no—
566C4×D4—24no—
567C4×D4—24no—
568C4×D4—24no—
569C4×D4—24no—
570C4×D4—24no—
571C4×D4—24no—
572C4×D4—216no—
573C4×D4—216no—
574C4×D4—28no—
575C4×D4—28no—
576C4×D4—216no—
577C4×D4—216no—
578C4×D4—28no—
579C4×D4—28no—
580C4×D4—216no—
581C4×D4—216no—
582C4×D4—24no—
583C4×D4—24no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4—24no—
587C4×D4—24no—
588C4×D4—24no—
589C4×D4—24no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—216no—
595C4×D4—216no—
596C4×D4C2414yes—
597C4×D4C2414yes—
598C4×D4C2414yes—
599C4×D4C2414yes—
600C4×D4C24116yes—
601C4×D4C24116yes—
602#117—22no—
603#117—22no—
604#117—28no—
605#117—28no—
606#117—28no—
607#117—28no—
608#117—216no—
609#117—216no—
610#117—216no—
611#117—24no—
612#117—216no—
613#117—24no—
614#117—24no—
615#117—24no—
616#117C2×D418yes—
617#117C2414yes—
618#117C2414yes—
619#117C2418yes—
620C2×C4⋊C4—22no—
621C2×C4⋊C4—22no—
622C2×C4⋊C4—22no—
623C2×C4⋊C4—22no—
624C2×C4⋊C4—28no—
625C2×C4⋊C4—28no—
626C2×C4⋊C4C2×D412yes—
627C2×C4⋊C4C2×D412yes—
628C2×C4⋊C4C2×D414yes—
629C2×C4⋊C4C2×D414yes—
630C2×C4⋊C4C2×D412yes—
631C2×C4⋊C4C2×D412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—216no—
640C2×C22⋊C4C2×D414yes—
641C2×C42—22no—
642C2×C42—22no—
643C2×C42—22no—
644C2×C42—216no—
645C2×C42—24no—
646C2×C42—24no—
647C2×C42—24no—
648C2×C42—24no—
649C2×C42C2×D412yes—
650C2×C42C2×D412yes—
651C2×C42C2×D411yescharacteristic
652C2×C42C2×D411yescharacteristic
653C2×C42C2414yes—
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658#107C2414yes—
659#107C2414yes—
660#106C2418yes—
661C4⋊C8C2411yescharacteristic
662C4⋊C8C2411yescharacteristic
663C4⋊C8C2412yes—
664C4⋊C8C2412yes—
665C4⋊C8C2414yes—
666C4⋊C8C2414yes—
667C4⋊C8C2412yes—
668C4⋊C8C2418yes—
669C4⋊C8C2418yes—
670C4⋊C8C24116yes—
671#103C2418yes—
672#103C2418yes—
673#103C2418yes—
674#103C2418yes—
675#103C2418yes—
676#103C2418yes—
677#102C2418yes—
678#102C2418yes—
679#102C2418yes—
680#102C2418yes—
681#102C2418yes—
682#102C2418yes—
683#97C2418yes—
684#97C24116yes—
685C4×C8C2414yes—
686C4×C8C2414yes—
687C4×C8C2418yes—
688C4×C8C2418yes—
689C24—24no—
690C24—22no—
691C24C22×D411yescharacteristic
692#41—216no—
693#41—28no—
694#41—28no—
695#41—216no—
696#41—28no—
697#41—216no—
698#41—28no—
699#41—216no—
700#41—48no—
701#41—416no—
702#41—48no—
703#41—416no—
704#41—816no—
705#41—816no—
706C2×Q8—22no—
707C2×Q8—24no—
708C2×Q8—24no—
709C2×Q8—28no—
710C2×Q8—24no—
711C2×Q8—28no—
712C2×Q8—44no—
713C2×Q8—82no—
714C2×Q8C22×D414yes—
715C2×Q8C22×D418yes—
716C2×Q8C22×D414yes—
717C2×Q8C2518yes—
718C2×Q8C2514yes—
719C2×D4—24no—
720C2×D4—28no—
721C2×D4—24no—
722C2×D4—28no—
723C2×D4—22no—
724C2×D4—24no—
725C2×D4—24no—
726C2×D4—24no—
727C2×D4—216no—
728C2×D4—216no—
729C2×D4—24no—
730C2×D4—24no—
731C2×D4—24no—
732C2×D4—28no—
733C2×D4—24no—
734C2×D4—28no—
735C2×D4—48no—
736C2×D4—416no—
737C2×D4—84no—
738C2×D4—84no—
739C2×D4C2518yes—
740C2×D4C2514yes—
741C22×C4—22no—
742C22×C4—24no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—24no—
746C22×C4—24no—
747C22×C4—24no—
748C22×C4—28no—
749C22×C4—28no—
750C22×C4—24no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—216no—
754C22×C4—216no—
755C22×C4—42no—
756C22×C4—48no—
757C22×C4—416no—
758C22×C4—84no—
759C22×C4—81no—
760C22×C4—84no—
761C22×C4C22×D412yes—
762C22×C4C22×D411yescharacteristic
763C22×C4C22×D412yes—
764C22×C4C22×D412yes—
765C22×C4C22×D412yes—
766C22×C4C22×D411yescharacteristic
767C22×C4C22×D411yescharacteristic
768C22×C4C22×D411yescharacteristic
769C22×C4C22×D414yes—
770C22×C4C22×D414yes—
771C22×C4C22×D411yescharacteristic
772C22×C4C22×D412yes—
773C22×C4C2×#4114yes—
774C22×C4H(5,𝔽2)14yes—
775C22×C4C2512yes—
776C22×C4C2511yescharacteristic
777Q16—216no—
778Q16—28no—
779Q16—48no—
780Q16—48no—
781Q16—48no—
782SD16—232no—
783SD16—216no—
784SD16—48no—
785SD16—48no—
786SD16—48no—
787SD16—48no—
788SD16—416no—
789D8—216no—
790D8—28no—
791D8—48no—
792D8—48no—
793D8—48no—
794M16—28no—
795M16C2×#41116yes—
796C2×C8—28no—
797C2×C8—28no—
798C2×C8—24no—
799C2×C8—24no—
800C2×C8—24no—
801C2×C8C2×#4118yes—
802C2×C8C2512yes—
803C2×C8C2512yes—
804C2×C8C2514yes—
805C2×C8C2514yes—
806C2×C8C2514yes—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—24no—
813C4⋊C4—216no—
814C4⋊C4—216no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—216no—
820C4⋊C4—216no—
821C4⋊C4C22×D418yes—
822C4⋊C4C22×D418yes—
823C4⋊C4C22×D414yes—
824C4⋊C4C22×D418yes—
825C4⋊C4C22×D4116yes—
826C4⋊C4C22×D418yes—
827C4⋊C4C22×D418yes—
828C4⋊C4C22×D414yes—
829C4⋊C4C2514yes—
830C4⋊C4C2514yes—
831C22⋊C4—24no—
832C22⋊C4—24no—
833C22⋊C4—28no—
834C22⋊C4—28no—
835C22⋊C4—24no—
836C22⋊C4—24no—
837C22⋊C4—216no—
838C22⋊C4—216no—
839C22⋊C4—24no—
840C22⋊C4—24no—
841C22⋊C4—28no—
842C22⋊C4—28no—
843C22⋊C4—216no—
844C22⋊C4—216no—
845C22⋊C4—216no—
846C22⋊C4—216no—
847C22⋊C4C22×D4116yes—
848C42—24no—
849C42—24no—
850C42—24no—
851C42—24no—
852C42—24no—
853C42—216no—
854C42—216no—
855C42—24no—
856C42C22×D412yes—
857C42C22×D412yes—
858C42C22×D412yes—
859C42C22×D412yes—
860C42C22×D411yescharacteristic
861C42C22×D412yes—
862C42C22×D418yes—
863C42C22×D411yescharacteristic
864C42C2511yescharacteristic
865C42C2511yescharacteristic
866C42C2518yes—
867C42C2512yes—
868C23—24no—
869C23—28no—
870C23—41no—
871C23—41no—
872C23—44no—
873C23—48no—
874C23—82no—
875C23—82no—
876C23—84no—
877C23—84no—
878C23#55014yes—
879C23C23×D411yescharacteristic
880C23C23×D412yes—
881Q8—28no—
882Q8—24no—
883Q8—28no—
884Q8—24no—
885Q8—28no—
886Q8—44no—
887Q8—48no—
888Q8—44no—
889Q8—48no—
890D4—24no—
891D4—28no—
892D4—24no—
893D4—28no—
894D4—48no—
895D4—48no—
896D4—416no—
897D4—48no—
898D4—416no—
899D4—48no—
900D4—44no—
901D4—48no—
902D4—84no—
903D4—84no—
904D4—816no—
905D4—816no—
906C2×C4—24no—
907C2×C4—22no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—24no—
911C2×C4—28no—
912C2×C4—41no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—41no—
916C2×C4—42no—
917C2×C4—41no—
918C2×C4—44no—
919C2×C4—44no—
920C2×C4—48no—
921C2×C4—44no—
922C2×C4—48no—
923C2×C4—48no—
924C2×C4—48no—
925C2×C4—416no—
926C2×C4—48no—
927C2×C4—416no—
928C2×C4—84no—
929C2×C4—84no—
930C2×C4—816no—
931C2×C4—816no—
932C2×C4—82no—
933C2×C4—82no—
934C2×C4#55018yes—
935C2×C4#55014yes—
936C2×C4C23×D411yescharacteristic
937C2×C4C23×D412yes—
938C2×C4C23×D412yes—
939C2×C4C23×D418yes—
940C2×C4C23×D418yes—
941C2×C4C23×D411yescharacteristic
942C2×C4C23×D411yescharacteristic
943C2×C4C23×D411yescharacteristic
944C2×C4C23×D412yes—
945C2×C4C23×D411yescharacteristic
946C2×C4C22×#4112yes—
947C2×C4C22×#4114yes—
948C2×C4C2×H(5,𝔽2)12yes—
949C2×C4C2×H(5,𝔽2)14yes—
950C2×C4C2611yescharacteristic
951C8—22no—
952C8—24no—
953C8—22no—
954C8—24no—
955C8C22×#4118yes—
956C22—21no—
957C22—22no—
958C22—21no—
959C22—22no—
960C22—44no—
961C22—44no—
962C22—48no—
963C22—44no—
964C22—48no—
965C22—44no—
966C22—48no—
967C22—88no—
968C22—168no—
969C22C2×#55014yes—
970C22C2×#55012yes—
971C22C24×D411yescharacteristic
972C4—22no—
973C4—21no—
974C4—28no—
975C4—22no—
976C4—21no—
977C4—21no—
978C4—28no—
979C4—44no—
980C4—44no—
981C4—44no—
982C4—48no—
983C4C2×#55012yes—
984C4C2×#55014yes—
985C4#358412yes—
986C4C23×#4111yescharacteristic
987C4C22×H(5,𝔽2)11yescharacteristic
988C2—24no—
989C2—22no—
990C2—84no—
991C2—88no—
992C2C22×#55011yescharacteristic
993C2C2×#358411yescharacteristic
994C2#6309011yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutator, Frattini, cosocleC2×C4C26
socleC22C24×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×#533 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #62815C2semidirect
2. #61424C2semidirect
3. #61423C2semidirect
4. #61422C2semidirect
5. #61421C2semidirect
6. #61420C2semidirect
7. #61419C2semidirect
8. #61401C2semidirect
9. #61401C2semidirect
10. #61393C2semidirect
11. #60643C2semidirect
12. #60639C2semidirect
13. #60422C2semidirect
14. C2×#3035C2semidirect
15. C2×#2962C2semidirect
16. #60161C2semidirect
17. C4×#575C2semidirect
25. #3510C22semidirect
26. #3509C22semidirect
27. #3508C22semidirect
28. #3507C22semidirect
29. #3507C22semidirect
30. #3506C22semidirect
31. #3506C22semidirect
34. #3480C22semidirect
35. #3480C22semidirect
45. #3403C22semidirect
46. #3403C22semidirect
47. #3402C22semidirect
48. #3402C22semidirect
49. #3401C22semidirect
50. #3401C22semidirect
51. #3401C22semidirect
52. #3400C22semidirect
53. #3400C22semidirect
54. #3399C22semidirect
55. #3399C22semidirect
56. #3398C22semidirect
57. #3398C22semidirect
58. #3397C22semidirect
59. #3397C22semidirect
60. #3396C22semidirect
61. #3396C22semidirect
62. #3395C22semidirect
63. #3394C22semidirect
64. #3394C22semidirect
65. #3393C22semidirect
66. #3393C22semidirect
67. #3392C22semidirect
68. #3391C22semidirect
69. #3156C22semidirect
70. #3155C22semidirect
71. #3154C22semidirect
72. #3154C22semidirect
73. #3153C22semidirect
74. #3152C22semidirect
75. #3151C22semidirect
76. #3150C22semidirect
77. #3150C22semidirect
78. #3147C22semidirect
79. #3147C22semidirect
80. #3046C22semidirect
81. #3046C22semidirect
82. #3045C22semidirect
83. #3045C22semidirect
84. #3044C22semidirect
85. #3043C22semidirect
86. #3042C22semidirect
87. #3041C22semidirect
91. #3035C22semidirect
92. #3035C22semidirect
93. #3035C22semidirect
94. #3035C22semidirect
95. #3035C22semidirect
96. C2×#464C22semidirect
97. C2×#462C22semidirect
98. C2×#460C22semidirect
99. C2×#463C22semidirect
100. C2×#461C22semidirect
101. C2×#459C22semidirect
102. #2962C22semidirect
103. #2962C22semidirect
104. #2962C22semidirect
105. C2×#446C22semidirect
106. C2×#446C22semidirect
107. C2×C8×Q8C22semidirect
108. #2947C22semidirect
109. #2947C22semidirect
110. #2946C22semidirect
111. #2946C22semidirect
112. C4×#137C22semidirect
113. C4×#137C22semidirect
114. C4×AGL(1,ℤ/8)C22semidirect
115. C4×AGL(1,ℤ/8)C22semidirect
116. #2943C22semidirect
117. #2943C22semidirect
118. C4×#135C22semidirect
119. C4×#135C22semidirect
458. C2×M16#41semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#628152
#614242
#614232
#614222
#614212
#614202
#614192
#614012
#613932
#606432
#606392
#604222
C2×#30352
C2×#29622
#601612
C4×#5752